Morales–Pak–Panova product formula for shifted skew tableaux

Let $n,a,b\geq 0$ and $m\geq 1$. Define the shifted skew shape $\pi=\mathbf{V}(n,a,b,m)$ by

$$\lambda=((n+a+b,n+a+b-1,\dots,b+1)+(m-1)\delta_{n+a})^*,\qquad \mu=(\delta_{a+1})^*,$$

where $\nu^*$ denotes the shifted Young diagram of a strict partition $\nu$. Let $g^\pi$ be the number of standard Young tableaux of shape $\pi$, let

$$\gimel(n)=\prod_{i=1}^{\lfloor n/2\rfloor}(n-2i)!,$$

let $D$ be the set of cells $(i,n+j)$ with $1\leq i\leq j\leq n$, and let $h_{\lambda^*}(i,j)$ denote the shifted hook length. Morales–Pak–Panova's conjecture. One has

$$g^\pi=\frac{|\pi|!}{2^a}\cdot\frac{\Phi(n+2a)\Phi(a)}{\Phi(2a)\Phi(n+a)}\cdot\frac{\gimel(2a)\gimel(n)}{\gimel(n+2a)}\prod_{(i,j)\in\lambda\backslash D}\frac{1}{h_{\lambda^*}(i,j)},$$

where $\Phi(r)=\prod_{i=1}^{r-1}i!$. This is a further conjectured product formula for standard tableaux of a structured shifted skew shape; the supplied source gives no resolution, so its status is left open.